Hiya I can definitely relate. In the very early stage where I made the assumption that my T had had this perfect amazing life, but that actually wasn't the case at all. Because of my experiences in life, I know now I would not be able to bond the same way to someone who hadn't gone through their own devastation or who could not discuss that with me.

I also know that therapy is fruitless (in terms of making real change) for me if I can't have communication outside the appointment. The spark of the deeper connection just goes out.

I know you say you feel it would just be the same with another therapist, but maybe you could find one who self discloses more and offers in between session contact?